Pierre Van MOERBEKE
(Louvain University and Clay Mathematical Institute)
Random permutations and matrices, and integrable systems
This mini-course will cover the following subjects:
- Longest increasing sequences in random permutations and words
- The spectrum of random matrices
- Large random permutations and large random matrices: asymptotics
Further References:
- P. van Moerbeke,
``Integrable lattices: random matrices and random
permutations'',
in Random matrices and their applications,
Mathematical
Sciences research Institute Publications
Vol.
40,
Cambridge University
Press,
pp. 321-406, (2001).
-
M. Adler and P. van Moerbeke, ``Hermitian, symmetric and symplectic random
ensembles: PDE's for the distribution of the spectrum'', Annals of
Mathematics, 153 (2001) 149-189;
math-ph/0009001.
-
A. Borodin, A. Okounkov and G. Olshanski, ``Asymptotics of Plancherel
measures for symmetric groups'', J. Amer. Math. Soc. 13 (2000)
481--515;
math.CO/9905032.
-
C.A. Tracy and H. Widom, ``Level-Spacings distribution and the Airy kernel'',
Comm. Math. Phys., 159 (1994) 151-174;
hep-th/9211141.